Line two baking sheets with parchment paper. Place the Cadbury Mini Eggs inside a folded kitchen towel and gently tap with a rolling pin or skillet until broken into a mix of chunky and small bits; set aside a handful of the larger pieces for topping.
In a medium bowl, whisk together the flour, baking soda, fine sea salt, and espresso powder.
In a large mixing bowl, beat the butter, brown sugar, and granulated sugar on medium speed until light and creamy, about 2 minutes, scraping the bowl once.
Beat in the egg, then the egg yolk, followed by the vanilla, mixing just until smooth.
Add the dry ingredients in two additions on low speed, stopping when a few streaks of flour remain. Fold in the mini chocolate chips and about three-quarters of the chopped Mini Eggs with a spatula.
Cover and chill the dough for 20 minutes to firm slightly and hydrate the flour.
While the dough chills, preheat the oven to 365°F (185°C) with a rack in the center.
Scoop the dough into 2-tablespoon mounds (about a medium cookie scoop) and arrange on prepared sheets, spacing about 2 1/2 inches apart. Lightly press a few reserved Mini Egg pieces onto the tops for a colorful finish.
Bake one sheet at a time for 11–13 minutes, rotating the pan halfway through. The edges should be set and golden while the centers remain pale with a soft gloss.
Remove from the oven and rap the baking sheet once on the counter to encourage crinkly edges. Sprinkle a tiny pinch of flaky sea salt over each cookie if using. Cool on the sheet for 10 minutes before transferring to a wire rack to cool completely.